On Lempert functions in .
Jarnicki, Witold (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Jarnicki, Witold (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Zhangjian Hu (1996)
Colloquium Mathematicae
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Hatori, Osamu, Kasuga, Kazuhiro (2009)
Banach Journal of Mathematical Analysis [electronic only]
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Engliš, Miroslav (2005)
Journal of Lie Theory
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Luis Gallardo (2000)
Acta Arithmetica
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1. Introduction. The Waring problem for polynomial cubes over a finite field F of characteristic 2 consists in finding the minimal integer m ≥ 0 such that every sum of cubes in F[t] is a sum of m cubes. It is known that for F distinct from ₂, ₄, , each polynomial in F[t] is a sum of three cubes of polynomials (see [3]). If a polynomial P ∈ F[t] is a sum of n cubes of polynomials in F[t] such that each cube A³ appearing in the decomposition has degree < deg(P)+3, we say that P is...
Binyamin Schwarz, Uri Srebro (1996)
Banach Center Publications
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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on which are balls with respect to the complex norm in are those centered at the origin.
Kilic, Nayil (2010)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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T. Pezda (1994)
Acta Arithmetica
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1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple of distinct elements of R is called a cycle of f if for i=0,1,...,k-2 and . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number , depending only on the degree N of K. In this...
Tadeusz Poreda
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CONTENTSIntroduction . . . . . . . . 5I. Fundamental problems for generalized differential equations at nonsingular points§1. Introduction . . . . . . . . 6§2. Cauchy problem at nonsingular points for generalized differential equations of the first order . . . . . . . . 6§3. Dependence of solution on parameters and initial conditions . . . . . . . . 8II. Total solutions of generalized linear differential equations§1. Introduction . . . . . . . . 11§2. Form of solutions of generalized...
Krzysztof Oleszkiewicz (1996)
Fundamenta Mathematicae
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The classical theorem of Borsuk and Ulam [2] says that for any continuous mapping there exists a point such that f(-x) = f(x). In this note a discrete version of the antipodal theorem is proved in which is replaced by the set of vertices of a high-dimensional cube equipped with Hamming’s metric. In place of equality we obtain some optimal estimates of which were previously known (as far as the author knows) only for f linear (cf. [1]).
J. P. Bell, P. B. Borwein, L. B. Richmond (1998)
Acta Arithmetica
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We estimate the maximum of on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when is or when is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when is j. In contrast we show, under fairly general conditions, that the maximum is less than , where r is an arbitrary positive number. One consequence...
Gerhard Keller (1996)
Fundamenta Mathematicae
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For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties: 1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in . The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure. 2. The omega-limit of Lebesgue-a.e point in is , but for a residual set of points in the omega...
Greshnov, A.V. (2001)
Sibirskij Matematicheskij Zhurnal
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